During metal cutting, the chip thickness ratio

Explanation:

Chip thickness ratio / Cutting ratio (r):

It is the ratio of chip thickness before cut (t1) to the chip thickness after cut (t2).

\(r=\frac{Chip\;thickness\;before\;cut\;(t_1)}{Chip\;thickness\;after\;cut\;(t_2)}\Rightarrow \frac{uncut\;chip\;thickness}{chip\;thickness}\)

chip thickness after the cut (t2) is always greater than the chip thickness before the cut (t1), ∴ r is always < 1, i.e. the uncut chip thickness value is less than the chip thickness value.

Assuming volume to be constant:

t1b1L1 = t2b2L2

\(\frac{t_1}{t_2}=\frac{L_2}{L_1}\;\;\;\;(\because b_1=b_2)=\left(\frac{\text {length of chip}}{\text {length of uncut chip}}\right)\)

as t2 > t1, ∴ L2 < L1 i.e. length after cut is less than the length before the cut.

Assuming discharge to be constant:

t1b1V = t2b2Vc

\(\frac{t_1}{t_2}=\frac{V_c}{V}\;\;\;\;(\because b_1=b_2)=\frac{Chip \ Velocity}{Cutting \ Velocity}\)

as t2 > t1, ∴ V > Vc i.e. cutting velocity is greater than the chip velocity.